Multi-level μ-finite element analysis for human bone structures

Abstract

Using microarchitectural bone imaging, it is now possible to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. In combination with microstructural finite element (μFE) analysis this could provide a powerful tool to improve strength assessment and individual fracture risk prediction. However, the resulting μFE models are very large and require dedicated solution techniques. Therefore, in this paper we investigate the efficient solution of the resulting large systems of linear equations by the preconditioned conjugate gradient algorithm. We detail the implementation strategies that lead to a fully parallel finite element solver. Our numerical results show that a human bone model of about 5 million elements can be solved in about a minute. These short solution times will allow to assess the mechanical quality of bone in vivo on a routine basis. Furthermore, our highly scalable solution methods make it possible to analyze the very large models of whole bones measured in vitro, which can have up to 1 billion degrees of freedom. © Springer-Verlag Berlin Heidelberg 2007.